Abstract

We report the design and experimental testing of a high-spatial-resolution nulling microellipsometer. This microellipsometer design is based on the previously reported principle of rotational polarization symmetry to improve the signal-to-noise ratio of spatially resolved ellipsometric measurements. Through the use of an electro-optic polarization rotator, a null detection scheme is made possible and implemented. Surface profiling of a lithographically patterned microstructure is demonstrated with the nulling microellipsometer. A lateral spatial resolution of 0.48μm is calculated with a numerical aperture of 0.9 and an illumination wavelength of 632.8nm.

© 2010 Optical Society of America

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2009

2008

2007

2006

2005

F. Linke and R. Merkle, “Quantitative ellipsometry microscopy at the silicon-air interface,” Rev. Sci. Instrum. 76, 063701 (2005).
[CrossRef]

2002

Q. Zhan and J. R. Leger, “Microellipsometer with radial symmetry,” Appl. Opt. 41, 4630-4637 (2002).
[CrossRef] [PubMed]

Q. Zhan and J. R. Leger, “Interferometric measurement of Berry's phase in space-variant polarization manipulations,” Opt. Commun. 213, 241-245 (2002).
[CrossRef]

1999

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45-R56 (1999).
[CrossRef]

1998

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, and J. Opsal, “Characterization of titanium nitride (TiN) films on various substrate using spectrophotometry, beam profile reflectometry, beam profile ellipsometry, and spectroscopic beam profile ellipsometry,” Thin Solid Films 313-314, 308-313 (1998).
[CrossRef]

1996

1994

1986

M. Erman and J. B. Theeten, “Spatially resolved ellipsometry,” J. Appl. Phys. 60, 859-873 (1986).
[CrossRef]

Amra, C.

Arnaud, L.

Arwin, H.

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

Chazallet, F.

Chegal, W.

S. Ye, Y. K. Kwak, S. H. Cho, Y. J. Cho, and W. Chegal, “Development of a focused-beam ellipsometer based on a new principle,” in Frontiers of Characterization and Metrology for Nanoelectronics, D. G. Seiler, A. C. Diebold, R. McDonald, C. M. Gamer, D. Herr, R. P. Khosla, and E. M. Secula, ed. (American Institute of Physics, 2007), pp. 69-73.

Chen, J.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, and J. Opsal, “Characterization of titanium nitride (TiN) films on various substrate using spectrophotometry, beam profile reflectometry, beam profile ellipsometry, and spectroscopic beam profile ellipsometry,” Thin Solid Films 313-314, 308-313 (1998).
[CrossRef]

Chen, K.

Chen, L.

Cho, S. H.

S. Ye, Y. K. Kwak, S. H. Cho, Y. J. Cho, and W. Chegal, “Development of a focused-beam ellipsometer based on a new principle,” in Frontiers of Characterization and Metrology for Nanoelectronics, D. G. Seiler, A. C. Diebold, R. McDonald, C. M. Gamer, D. Herr, R. P. Khosla, and E. M. Secula, ed. (American Institute of Physics, 2007), pp. 69-73.

Cho, Y. J.

S. Ye, Y. K. Kwak, S. H. Cho, Y. J. Cho, and W. Chegal, “Development of a focused-beam ellipsometer based on a new principle,” in Frontiers of Characterization and Metrology for Nanoelectronics, D. G. Seiler, A. C. Diebold, R. McDonald, C. M. Gamer, D. Herr, R. P. Khosla, and E. M. Secula, ed. (American Institute of Physics, 2007), pp. 69-73.

Deumié, C.

Erman, M.

M. Erman and J. B. Theeten, “Spatially resolved ellipsometry,” J. Appl. Phys. 60, 859-873 (1986).
[CrossRef]

Fanton, J.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, and J. Opsal, “Characterization of titanium nitride (TiN) films on various substrate using spectrophotometry, beam profile reflectometry, beam profile ellipsometry, and spectroscopic beam profile ellipsometry,” Thin Solid Films 313-314, 308-313 (1998).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Modeling of data,” in Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1988), pp. 517-564.

Georges, G.

Holmes, R. D.

Huang, Y.

Humlicek, J.

J. Humlicek, “Polarized light and ellipsometry,” in Handbook of Ellipsometry, T. Harland and E. A. Irene, eds. (Springer, 2005), pp. 3-90.

Ishikawa, M.

Järrendahl, K.

Jenkins, T. E.

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45-R56 (1999).
[CrossRef]

Kozlovskaya, V.

Kwak, Y. K.

S. Ye, Y. K. Kwak, S. H. Cho, Y. J. Cho, and W. Chegal, “Development of a focused-beam ellipsometer based on a new principle,” in Frontiers of Characterization and Metrology for Nanoelectronics, D. G. Seiler, A. C. Diebold, R. McDonald, C. M. Gamer, D. Herr, R. P. Khosla, and E. M. Secula, ed. (American Institute of Physics, 2007), pp. 69-73.

Le Neindre, N.

Leger, J. R.

Q. Zhan and J. R. Leger, “Microellipsometer with radial symmetry,” Appl. Opt. 41, 4630-4637 (2002).
[CrossRef] [PubMed]

Q. Zhan and J. R. Leger, “Interferometric measurement of Berry's phase in space-variant polarization manipulations,” Opt. Commun. 213, 241-245 (2002).
[CrossRef]

Leng, J. M.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, and J. Opsal, “Characterization of titanium nitride (TiN) films on various substrate using spectrophotometry, beam profile reflectometry, beam profile ellipsometry, and spectroscopic beam profile ellipsometry,” Thin Solid Films 313-314, 308-313 (1998).
[CrossRef]

Linke, F.

F. Linke and R. Merkle, “Quantitative ellipsometry microscopy at the silicon-air interface,” Rev. Sci. Instrum. 76, 063701 (2005).
[CrossRef]

Liu, A.

Mendoza-Galván, A.

Merkle, R.

F. Linke and R. Merkle, “Quantitative ellipsometry microscopy at the silicon-air interface,” Rev. Sci. Instrum. 76, 063701 (2005).
[CrossRef]

Opsal, J.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, and J. Opsal, “Characterization of titanium nitride (TiN) films on various substrate using spectrophotometry, beam profile reflectometry, beam profile ellipsometry, and spectroscopic beam profile ellipsometry,” Thin Solid Films 313-314, 308-313 (1998).
[CrossRef]

Otsuki, S.

Plawsky, J. L.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Modeling of data,” in Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1988), pp. 517-564.

Pristinski, D.

Ritz, K.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, and J. Opsal, “Characterization of titanium nitride (TiN) films on various substrate using spectrophotometry, beam profile reflectometry, beam profile ellipsometry, and spectroscopic beam profile ellipsometry,” Thin Solid Films 313-314, 308-313 (1998).
[CrossRef]

See, C. W.

Senko, M.

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, and J. Opsal, “Characterization of titanium nitride (TiN) films on various substrate using spectrophotometry, beam profile reflectometry, beam profile ellipsometry, and spectroscopic beam profile ellipsometry,” Thin Solid Films 313-314, 308-313 (1998).
[CrossRef]

Siozade, L.

Somekh, M. G.

Sukhishvili, S. A.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Modeling of data,” in Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1988), pp. 517-564.

Theeten, J. B.

M. Erman and J. B. Theeten, “Spatially resolved ellipsometry,” J. Appl. Phys. 60, 859-873 (1986).
[CrossRef]

Tompkins, G. G.

G. G. Tompkins, A User's Guide to Ellipsometry (Academic, 1993).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Modeling of data,” in Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1988), pp. 517-564.

Wagner, P. C.

Ye, S.

S. Ye, Y. K. Kwak, S. H. Cho, Y. J. Cho, and W. Chegal, “Development of a focused-beam ellipsometer based on a new principle,” in Frontiers of Characterization and Metrology for Nanoelectronics, D. G. Seiler, A. C. Diebold, R. McDonald, C. M. Gamer, D. Herr, R. P. Khosla, and E. M. Secula, ed. (American Institute of Physics, 2007), pp. 69-73.

Zaghloul, A. R. M.

Zaghloul, Y. A.

Zerrad, M.

Zhan, Q.

Q. Zhan and J. R. Leger, “Microellipsometer with radial symmetry,” Appl. Opt. 41, 4630-4637 (2002).
[CrossRef] [PubMed]

Q. Zhan and J. R. Leger, “Interferometric measurement of Berry's phase in space-variant polarization manipulations,” Opt. Commun. 213, 241-245 (2002).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

M. Erman and J. B. Theeten, “Spatially resolved ellipsometry,” J. Appl. Phys. 60, 859-873 (1986).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45-R56 (1999).
[CrossRef]

Opt. Commun.

Q. Zhan and J. R. Leger, “Interferometric measurement of Berry's phase in space-variant polarization manipulations,” Opt. Commun. 213, 241-245 (2002).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

F. Linke and R. Merkle, “Quantitative ellipsometry microscopy at the silicon-air interface,” Rev. Sci. Instrum. 76, 063701 (2005).
[CrossRef]

Thin Solid Films

J. M. Leng, J. Chen, J. Fanton, M. Senko, K. Ritz, and J. Opsal, “Characterization of titanium nitride (TiN) films on various substrate using spectrophotometry, beam profile reflectometry, beam profile ellipsometry, and spectroscopic beam profile ellipsometry,” Thin Solid Films 313-314, 308-313 (1998).
[CrossRef]

Other

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, “Modeling of data,” in Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, 1988), pp. 517-564.

S. Ye, Y. K. Kwak, S. H. Cho, Y. J. Cho, and W. Chegal, “Development of a focused-beam ellipsometer based on a new principle,” in Frontiers of Characterization and Metrology for Nanoelectronics, D. G. Seiler, A. C. Diebold, R. McDonald, C. M. Gamer, D. Herr, R. P. Khosla, and E. M. Secula, ed. (American Institute of Physics, 2007), pp. 69-73.

G. G. Tompkins, A User's Guide to Ellipsometry (Academic, 1993).

J. Humlicek, “Polarized light and ellipsometry,” in Handbook of Ellipsometry, T. Harland and E. A. Irene, eds. (Springer, 2005), pp. 3-90.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977).

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Figures (9)

Fig. 1
Fig. 1

(a) Conceptual illustration of a conventional ellipsometer, (b) a single ellipsometric channel of the microellipsometer with the insertion of a high-NA objective lens, and (c) pupil plane view of the single channel and the idea of repeating the single channel symmetrically within the entire annular ring.

Fig. 2
Fig. 2

Conceptual diagram of a radially symmetric microellipsometer design. The two beam splitters are identical and form a beam-splitter pair (BP). BS1 and BS2 are two identical beam splitters paired such that the s-polarization for the first beam splitter (BS1) becomes the p-polarization for second beam splitter (BS2), and vice versa. The linear polarizer (LP) and the first quarter-wave plate (QWP) generate a circular polarization (CP). PR, polarization rotator. A radial analyzer (RA) is used due to polarization’s rotational symmetry.

Fig. 3
Fig. 3

Diagram of the electro-optic polarization rotator (PR). EOVR: electro-optic variable retarder.

Fig. 4
Fig. 4

Coordinate systems in the back focal plane of the objective.

Fig. 5
Fig. 5

Schematic of the microellipsometer instrumentation. The lock-in amplifier (LA) takes the signal and its reference in from the detector and a function generator (FG). The high-voltage amplifier (HVA) amplifies ( × 100 ) the dc-biased ac signal supplied by the FG. BP is a beam-splitter pair formed by pairing two identical beam splitters BS1 and BS2 (see Fig. 2) such that the s-polarization for the first beam splitter (BS1) becomes the p-polarization for second beam splitter (BS2) and vice versa. M, mirror; USB DAQ, USB data acquisition card.

Fig. 6
Fig. 6

Examples of (a) first-harmonic signal and (b) dc signal versus the dc bias voltage applied to the EO variable retarder for a Si O 2 thin film on a silicon substrate. Two null points of the first harmonic can be clearly identified.

Fig. 7
Fig. 7

AFM scan of microprisms that form the grating sample. A line scan of the microprism profile is shown at the bottom.

Fig. 8
Fig. 8

(a) Fitting of experimental measurements of ψ to the optical model data. (b) Fitting of experimental measurements of Δ to the optical model.

Fig. 9
Fig. 9

Microellipsometer thickness profile measurements (dashed and dotted curves) compared to the AFM profile measurement. The second microellipsometer measurement was performed to check the repeatability of the measurements.

Equations (12)

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T = Q ( λ / 4 ) π 2 P ( δ ) π 4 Q ( λ / 4 ) π 2 = R ( π / 2 ) ( 1 0 0 j ) R ( π / 2 ) R ( π / 4 ) ( 1 0 0 exp ( j δ ) ) R ( π / 4 ) ( 1 0 0 j ) = j exp ( j δ / 2 ) R ( δ / 2 ) ,
δ = 2 π λ 0 n 0 3 r 63 V ,
E in = ( 1 j ) .
E loc = R ( φ ) E in = ( cos φ sin φ sin φ cos φ ) ( 1 j ) = e j φ ( 1 j ) .
Φ = Φ bias + α m cos ω t ,
P = K { 1 + cos 2 ε cos [ 2 ( Φ bias + α m cos ω t + θ 0 ) ] } ,
cos [ 2 ( Φ bias + α m cos ω t + θ 0 ) ] cos 2 ( Φ bias + θ 0 ) ( 1 α m 2 + α m 2 cos 2 ω t ) 2 α m sin 2 ( Φ bias + θ 0 ) cos ω t .
P ( 0 ) = K [ 1 + cos 2 ε ( 1 α m 2 ) cos 2 ( Φ bias + θ 0 ) ] ,
P ( ω ) = 2 K α m cos 2 ε sin 2 ( Φ bias + θ 0 ) cos ( ω t + π ) ,
P ( 2 ω ) = K cos 2 ε α m 2 cos 2 ( Φ bias + θ 0 ) cos 2 ω t .
cos ( 2 ψ ) = cos ( 2 ε ) cos ( 2 θ o ) ,
tan ( Δ ) = tan ( 2 ε ) sin ( 2 θ o ) .

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